Universal spectral statistics in Wigner-Dyson, chiral and Andreev star graphs I: construction and numerical results

Details Universal spectral statistics in Wigner-Dyson, chiral and Andreev star graphs I: construction and numerical results Universal spectral statistics in Wigner-Dyson, chiral and Andreev star graphs I: construction and numerical results

2003-09-18

arxiv.org/abs/nlin/0309049v1

Nonlinear Sciences

Chaotic Dynamics

15 pages

Scientific paper

10.1103/PhysRevE.69.056219

In a series of two papers we investigate the universal spectral statistics of chaotic quantum systems in the ten known symmetry classes of quantum mechanics. In this first paper we focus on the construction of appropriate ensembles of star graphs in the ten symmetry classes. A generalization of the Bohigas-Giannoni-Schmit conjecture is given that covers all these symmetry classes. The conjecture is supported by numerical results that demonstrate the fidelity of the spectral statistics of star graphs to the corresponding Gaussian random-matrix theories.

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